Difference between revisions of "2024 AMC 8 Problems/Problem 13"
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| + | {{AMC8 box|year=2024|num-b=12|num-a=14}} | ||
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Revision as of 19:58, 26 January 2024
Buzz Bunny is hopping up and down a set of stairs, one step at a time. In how many ways can Buzz start on the ground, make a sequence of 
hops, and end up back on the ground?
(For example, one sequence of hops is up-up-down-down-up-down.)
Contents
Solution 1
Looking at the answer choices, you see that you can list them out. Doing this gets you:
UUDDUD
UDUDUD
UUUDDD
UDUUDD
UUDUDD
Counting all the paths listed above gets you 5 or B.
-ALWAYSRIGHT11
Solution 2
These numbers are clearly the Catalan numbers. Since we have 6 steps, we need the third Catalan number, which is 
.
~andliu766
Video Solution 1 (easy to digest) by Power Solve
Video Solution 2 by Math-X (First fully understand the problem!!!)
https://www.youtube.com/watch?v=Td6Z68YCuQw
~Math-X
Video Solution 3 by OmegaLearn.org
Video Solution by CosineMethod [🔥Fast and Easy🔥]
https://www.youtube.com/watch?v=-kCN6R9U944
See Also
| 2024 AMC 8 (Problems • Answer Key • Resources) | ||
| Preceded by Problem 12 |
Followed by Problem 14 | |
| 1 • 2 • 3 • 4 • 5 • 6 • 7 • 8 • 9 • 10 • 11 • 12 • 13 • 14 • 15 • 16 • 17 • 18 • 19 • 20 • 21 • 22 • 23 • 24 • 25 | ||
| All AJHSME/AMC 8 Problems and Solutions | ||
The problems on this page are copyrighted by the Mathematical Association of America's American Mathematics Competitions. 
